I work at the Chemistry Stockroom in my university so I have handy a little thing called Terri Towels. These things are twice the absorbing power of Bounty, very effective grease cleaners for screens, very soft on hands and things, and specially cleans dirt up well. I use one of these slightly damp and my MacBook's screen is left as new. I used them in my previous PC and now my Mac, they leave screens crystal clear and the smudges even keep off for a while.
Bad thing about Terri Towels is that they are expensive and are sold only by the case which contains 6 sets of 200 sheets. So I think I can call myself lucky me and my co-workers get to use these babies free.😉